This invention describes a novel application of cryptographic commitments and zero-knowledge techniques to the relationship between and investor and a portfolio manager. The interest of the portfolio manager is in earning high returns, so he may want to keep his exact portfolio and trading strategy secret. An investor, on the other hand, also requires mechanisms to ensure the honesty of the managers, and to check that the fund's risk characteristics are in line with his own risk preferences. This invention addresses the fundamental problem of how to control the flow of risk information to serve these distinct interests. We suggest that the tool described herein is particularly suited to hedge funds, which tend to be highly secretive and more loosely regulated, and whose risk characteristics may not be evident to the investor.
Comparison with Earlier Work: Cryptography has been applied to financial transactions before, in generic ways—for example, to enhance privacy or integrity of data—and in ways specific to transactions, for example, digital cash, and auction design. The cryptographic tools of commitment and zero-knowledge proofs have been used as components in identification schemes and digital signatures, and zero-knowledge proofs have also appeared as components in multi-party computations such as auctions. Within the financial sector, cryptography has been used to protect the integrity of transactional data, and to facilitate the transactions themselves. Additionally, cryptographic techniques have appeared as components of payment schemes, including digital cash. However, zero-knowledge proofs have never directly been used before as a component of a system to help ensure that an investment fund contains risk characteristics which are acceptable to an investor.
Previous work has provided security for financial transactions themselves. The present invention concerns the use of cryptographic techniques to allow a more finely-controlled release of financial information from an investment portfolio manager to an investor.
Similarly, there has been significant work in the field of financial risk modeling, and, for example, the construction of statistical models which describe how a portfolio's value depends on a set of economic factors in a set of hypothetical future scenarios. It is also in common practice to make risk characteristics of a portfolio available to an investor. Regardless of the financial models used, traditional methods of risk communication have not yet made use of cryptographic proof techniques to support the validity of the claimed risks, or as a tool to help prevent fraud.
The present invention may make use of standard cryptographic tools such as Pedersen Commitments and Interval Proofs. Similarly, the invention may make use of the financial risk tools of factor analysis and scenario analysis. This invention is new because it combines the two components in a non-obvious manner, to provide a new tool for the investor manager relationship. As background for the invention, we first review the mechanics of these tools and show how to assemble them into (zero knowledge) statements which are meaningful to the investor. For simplicity, we stick to well-known building blocks describing the invention, but do not wish to limit the scope of the invention to any particular cryptographic primitive, or financial model. We continue with the finance background.
Portfolios and Risk: Investors and fund managers have different interests with respect to release of information. An investment portfolio is just a collection of assets designed to store or increase wealth. In a managed fund, the investor turns over capital to a fund manager, an investment professional who buys, sells, and otherwise maintains the portfolio in return for a fee or commission. The assets often contain publicly-traded securities such as stocks, bonds, commodities, options, currency exchange agreements, mortgages, “derivative” instruments, as well as less liquid assets such as real estate, or collectibles. Examples of managed funds are pension funds, 401K plans, mutual funds, and hedge funds.
Every type of investment contains uncertainty and risk. Ultimately, the risk inherent in investments derives from the fact that the future market value depends on information which is not available: information concerning either unknown future events, or information concerning past events which has not been publicly disclosed or effectively analyzed. The charter of the fund manager is to manage these risks in accordance with the preferences of the investor.
Risk Factors: The finance profession has developed a plethora of models to define and estimate portfolio risks. A first description of a portfolio's risks includes a breakdown of the types of assets in the fund such as the proportion of capital invested in equity, debt, foreign currency, derivatives, and real estate. A further breakdown specifies the allocation by industry type or sector, or region for foreign investments.
The future value of an investment depends on such future unknown factors as corporate earnings for stocks, interest rates and default likelihood for bonds, monetary policy and the balance of trade for foreign currency, regional political stability for any foreign investment, re-financing rates for securitized mortgages, housing demand for real estate, etc.
Risk models identify such measurable risk factors, and study the dependence of the asset's value on each factor. Such factor exposures are estimated with statistical regression techniques, and describe not only the sensitivity to the factor but also how the variance, or volatility of a security depends on such correlated factors. Assembling such analysis for all securities in a portfolio, the fund manager has a method for quantatively understanding the relative importance of the risk factors his portfolio is exposed to. Another important tool, scenario analysis, is used to estimate the future value of a portfolio under a broad range of hypothetical situations.
Hedge Funds: To hedge against a risk is effectively to buy some insurance against an adversarial event. When two assets depend oppositely on the same risk factor, the combined value of the pair is less sensitive to that factor. A hedge fund is just a type of portfolio designed to have certain aggregate risk characteristics. Hedge funds may use leveraging techniques such as statistical arbitrage, i.e.—engaging in long and short positions in similarly behaving securities, hoping to earn a profit regardless of how the correlated securities behave.
Hedge funds are often large private investments and are more loosely regulated than publicly offered funds. (e.g., they need not register with the SEC). Such extra flexibility affords the possibility of exceeding the performance of more standard funds. For example, hedge funds often take a position contrary to the market consensus, effectively betting that a certain event will happen. When accompanied by superior information or analysis such bets can indeed have high expected value. Of course, highly leveraged funds can be extremely sensitive to a particular risk factor, and are thus also susceptible to extreme losses.
The high investment minimums, lax regulation and secrecy or “black box” nature of hedge funds has fostered an aura of fame and notoriety through their spectacular returns, spectacular losses, and opportunities for abuse. Recently, though, there has been interest in marketing hedge funds as viable opportunities for the average investor.
The Role of Information
Information and Asset Prices: A market assigns a value to an asset based on the prices in a steady steam of transactions. The information perceived to be relevant to the asset's value is compared to existing expectations and drives the supply, demand, and market price. The pivotal role of information is embodied in the efficient market hypothesis which states that if everyone has the same information, the collective brainpower of investors will reduce arbitrage opportunities, and force the market price to an equilibrium.
In the real world, not everyone has the same information, and the information asymmetries among parties significantly affect the behavior of asset prices in the market. The situation is worse for illiquid assets, for which one must rely on some adhoc fundamental analysis to estimate the value. Similarly, it is difficult to assign a robust value to an investment fund with opaque risk characteristics (such as a hedge fund). A greater knowledge of the actual risk profile of hedge funds would increase their usefulness in funds of funds, for example.
The Importance of Secrets: Certain investments, such as passive funds which track an index may have no requirement to protect the portfolio contents or trading patterns. Actively traded funds, on the other hand, have good reasons to maintain secrets. For example, revealing in advance an intention to purchase a large quantity of some security would drive the price up. A parallel can be made with corporations: Sharing technological, financial, and trade secrets would undermine the competitive advantage of a firm.
Especially relevant to our focus, if a hedge fund were exploiting a subtle but profitable arbitrage opportunity, revealing this strategy would quickly destroy the benefit, as other funds would copy the strategy until it was no longer profitable. Thus, a rational investor will support such constructive use of secrets.
The Importance of Transparency: Secrecy is also dangerous. The actions of a fund manager might not aim to create value for the investor! The danger of too much secrecy is that it also reduces barriers to theft, fraud, and other conflicts of interest. An example of corrupt behavior that might be discouraged by increased transparency is the practice of engaging in unnecessary trading motived by brokerage commissions. To combat this risk, individual investors require enough access to information about a company or fund to help ensure honest management, consistent with the creation of value.
Another kind of problem will arise if the investor is not aware of the kinds of risks his portfolio is exposed to. In this case it is impossible to tell if these risks are in line with his preferences. A fund manager might be motivated by a fee structure which encourages him to take risks that are not acceptable to the investor. When the fee structure or actual level of risk in the portfolio is not evident to the investor, a fund manager may legally pursue actions consistent with interests other than the investor's.
Aligning Interests: The above discussion concerning just how much risk information should be kept secret and how much should be revealed shows how difficult it is in practice to perfectly align the interests of investors and fund managers. The traditional approaches to mitigating this problem involve financial regulatory bodies such as the SEC, which seeks to institute reporting laws and support capital requirements that protect the investor, ideally without imposing too large a burden on the financial institution. In the case of hedge funds, the position of the SEC is that the interests of the investor are not adequately protected. Indeed, it has not been able to eliminate all fraud and conflict of interests arising in the context of hedge funds.
There are several requirements for a good set of mechanisms to align the interests of investors and managers. These include methods for the investor to ensure the honesty of the fund manager, methods for the investor to be aware of the fund's evolving risks, and contractual agreements and fee structures which discourage the manager from adding hidden risks. Finally, the mechanisms should not discourage the fund manager from fully exploiting any competitive advantage or superior analysis which he might have.
Finance and Cryptography
Previous Work: There are many existing applications of cryptography to financial infrastructure. The most significant practical applications involve well known aspects of securing the transactions themselves: providing authenticity of the parties, integrity and non-repudiation of the transactions, and confidentiality among the parties. Such applications all use cryptography in a generic way, not tailored to any particular requirements of finance.
More interesting advanced finance-related applications of cryptography include fair exchange, secure auctions, and digital anonymous cash. These applications use cryptography as a building block to compose cryptographic protocols which protect some aspect of a transaction, preserve some secret, or prove the correctness of a protocol step. The technique of sending non-interactive proofs relative to previously committed values is pervasive in protocol design.
New Contributions: IThe present invention concerns the release of information about the evolving portfolio's composition and risks. This kind of application has not previously appeared. The present invention concerns an additional mechanism which will help achieve a better balance of information sharing between fund managers and investors. The invention may be used to precisely control the level of transparency in an investment fund. The result is that the investor can ensure that an appropriate level and type of risk is taken, yet the fund can pursue competitive strategies which would not be possible if the restriction of perfect transparency were imposed.
Cryptographic commitments, and zero knowledge proofs provide versatile tools for precisely controlling the delivery of partial and verifiable pieces of information. The present invention concerns these methods in the context of financial risk management.
Long Perceived Need: The finance industry has long sought a mechanism to finely control the release of investment risks, in a way which respects private trading strategies, yet makes fraud difficult. It has long been recognized that portfolio secrecy and verifiability of investment risks and holding are at odds with one another. The famous Long Term Capital hedge fund default may be the most well known example of the dilemma posed by the conflicting advantages of keeping exact portfolio positions secret, and accurately communicating risks to investors. Indeed, before the present invention, it was generally assumed that investors would have to give up verifiability in order to participate in hedge fund strategies. The present invention can be used to provide a solution to a long standing problem; now, risk information can be communicated in a verifiable way to the investor, without eliminating the valuable technique of maintaining private trading strategies.